Expectations management is important when getting a chemical peel.
Salicylic acid peels tend to cause a burning sensation more commonly than other types of peels. The stinging may occur on the whole face. It tends to peak and then get better.
I tell my patients to expect to peel in 1-3 days. Not everyone experiences noticable peeling every time--this does not mean it's not working. The peeling usually stops in 1 week. I advise patients to moisturize with a bland lotion or cream at least 2-3 times a day after a peel and wear sunscreen daily.
Based on the above picture you may have had some crusting or just peeling skin that has not yet come off. Moisturize more frequently in this case and consider applying a topical steroids such as hydrocortisone (check with your doctor--of course).
This kind of peeling or crusting may occur if you had been using an exfoliating agent such as a retinoids, glycolic acid or salicylic acid product right before the peel or if you had a rash on your face when you got the peel.